Prescribed-Time Stabilization of High-Order Polynomial Time-Varying Nonlinear Systems

This article explores the problem of prescribed-time stabilization for a class of high-order polynomial nonlinear systems with unknown time-varying nonlinearities. The key technique behind the proposed strategy involves fixing the time-varying components to their bounded values before the prescribed time and establishing a new lemma to suppress the time-varying continuous functions in the investigated system. We design a continuous bounded feedback controller to address the singularities induced by infinite control gains at the prescribed time and to suppress the implicit effects of time variations. Superior to the existing prescribed-time stabilization results, our strategy achieves the states' convergence within the prescribed-time and the nontruncated run of controller simultaneously. We employ the wing rock motion to demonstrate the practicality and superiority of the developed strategies.